Not much difference really, which is why you see them placed in either place. Personal preference more than anything, and if you've only been training an LP, you don't have enough experience to have a personal preference yet so just pick one.
the grey book has them as a top set on intensity day (Friday), but Mark's online article, and other SSC blogs that outline the method, have the deadlifts as being on Monday after volume stuff.
Why the difference? What circumstances would warrant one vs the other?
Not much difference really, which is why you see them placed in either place. Personal preference more than anything, and if you've only been training an LP, you don't have enough experience to have a personal preference yet so just pick one.
I've always done DL on Friday/intensity day. Doing a heavy set of DL at the end of volume day once your deep into TM is really tough.